Given a positive integer n the k-fold divisor function dk(n) equals the number of ordered k-tuples of positive integers whose product equals n. In this article we study the variance of sums of d(k)(n) in short intervals and establish asymptotic formulas for the variance of sums of d(k)(n) in short intervals of certain lengths for k = 3 and for k >= 4 under the assumption of the Lindelof hypothesis.
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